Hi DavidNegranu
it's pretty difficult to answer your questions... for example, a minraise on the river is much much more stronger than a minraise on the turn, and in the same way a minraise on the turn is much more stronger than a minraise on the flop. so i guess as a general rule of thumb you should interpret it as stronger the further the hand progresses but this is not necessarily always the case...
for some people a minraise *might* be a way of "figuring out where they are at in the hand" - similar to those annoying donkbets - or it might be with a TP hand. or it might be a total bluff. or it might be the nuts. most of the time a minraise will be polarising i.e. either the nuts or complete air (or a draw), but i would definitely not be surprised to see some weirdly played middle pair hand playing this way as well.
so what can you do? there are a couple of things. first off, understand that it really depends on who your opponents are: take notes on how people play their top pairs, how they play their draws, their air, and then how they play the nuts. this should give you some insight - for example if you see someone slowplaying a monster a couple of times, it is very possible that they tend to always do this and therefore a minraise from this player might be weighted heavily towards non-nutted hands (however not necessarily bluffs).
next (and i definitely recommend this), you could go into your holdem manager/pokertracker. take as big a sample of hands as you can, so preferably your lifetime graph. then find a filter for the following:
1) situations where you were minraised on the flop + saw a showdown
2) situations where you were minraised on the turn + saw a showdown
3) situations where you were minraised on the river + saw a showdown
not sure exactly what the names of these filters will be but it shouldnt be too difficult. once you've done that, take a pen/paper/notepad/excel and write down what you see people do this with. in all likelihood you'll see a wide range of craziness, but a general pattern should emerge.
also, something else you should do is work on your understanding of board textures. most importantly, why are you betting with air on board textures where you will get played back at? surely the logical thing would be to take a look at these spots and simply stop investing money. for example, i wouldnt expect too many minraises on a K♠7♥4♣ board. conversely, i'd expect many less folds on a 8♦6♦5♠ board. on a dry board it is difficult for anyone to have anything so most of the time the PFA will take the pot down with a cbet. on the other hand, a wet board hits the preflop-caller a fair amount and therefore we should expect less folds and more minraises. this is ofc very generally speaking but your questions are quite general themselves.
with that said, if a fishy player is minraising AND he is very passive (we should assume passivity as a default), then the easy solution is to just let him take his pot - he most likely has a hand. if a fishy & aggressive guy is minraising, he can also have a hand but it's really impossible to say. if a competent and solid player is minraising you then my guess would either be that he's figured out that you fold - even to a minraise - and therefore his bluff doesnt need to be very big to work against you.... or most likely he's actually not as competent as you first thought ♦
hope that helps. and maybe some of the other guys here could give you their opinions/experiences because i think we all have our ways of dealing with these spots.